What measures central location using the value in the middle after data sorting?

The median is the measure of central location that represents the value in the middle after the data has been sorted. To find the median, you first arrange the data points in ascending or descending order. If there is an odd number of observations, the median is simply the middle value. In the case of an even number of observations, the median is calculated by taking the average of the two middle values. This property makes the median a robust measure of central tendency, as it is not affected by extreme values or outliers in the dataset.

In contrast, the mean is calculated by adding all the values together and dividing by the number of values, which can skew the result if extreme outliers are present. The mode is the value that occurs most frequently in a dataset, which is a different way to interpret central location and does not involve sorting the data. The range, on the other hand, measures the spread of the data by calculating the difference between the highest and lowest values, and it does not provide information about the central tendency of the data.